Read these message boards and you'll get a lot of great ideas. But remember to take everything with a grain of salt. We're all very opinionated so you might like something that others don't. Be sure to weigh your feelings when reading opinions.
I would suggest and highly recommend seeing Glacier Bay. It's spectacular and will narrow down your choices a lot which can make things simpler.
IMHO NCL is the best line for the money. You will find many anti-NCL people on these sites. We've gone to Alaska on NCL, HAL, and Celebrity. NCL might be a 1/2 step behind but they're also innovative (freestyle) and less expensive. For a first cruise you'll be happy I'd say.
There is certainly less chance of good weather in September. However we've always gone in August and run into rain on each trip. Heck, it's in a rain forest! But if you're prepared for it and pack ok you'll probably be allright in Sept.
I'm a balcony person too (remember...grain of salt). There will be many who disagree with me on paying extra for a balcony. To me the scenery is so great and never ending that I want to miss as little as possible, even when getting dressed.
I suggest find a decent cruise specialist agent. Many are mentioned on these sites. They will have the best deals (in our case cheaper than the lines directly) and the best cabin locations.
Try going to Yahoo travel or expedia or Travelocity. Plug into the cruise section for Alaska. You'll see all the options. Then you can begin to narrow your choices down as well. Once you've chosen a route and line and ship, it'll be much easier to get quotes from the agents. And do get a few quotes. You'll be surprised at the differences.
Good luck on your marriage and I'm sure all of us opinionated cruisers will agree......Alaska is spectacular and you won't be dissapointed no matter what you choose.